1. Field of the Invention
The present invention relates to a method of evaluating an energy loss of a golf ball. More particularly, the present invention is intended to visualize the energy loss generated in the interior of the golf ball not by making the golf ball as an experiment but by a simulation.
2. Description of the Related Art
The flight distance of the golf ball is one of its important performances demanded by a golfer. The golf ball that can fly a long distance gives the golfer a refreshing feeling and contributes to getting a high score. To increase the flight distance, it is necessary to improve the restitution performance of the golf ball.
Therefore in designing the golf ball, the restitution performance of the golf ball when it is hit is one of the main items that should be evaluated. Thus to improve the restitution performance of the golf ball, many proposals have been hitherto made.
Considered in one proposal is to pay attention to an energy loss generated in the interior of the golf ball when it is hit. More specifically, when a hitting object impacts (collides with) the golf ball, the golf ball deforms greatly and separates from the hitting object, thus generating a restitution. It is known that the restitution coefficient of the golf ball at this time is greatly affected by the energy loss generated in the interior of the golf ball when the hitting object collides with the golf ball.
It is also known that when the hitting object does not strike against the sweet spot of the golf ball, an energy generated at the time of the collision therebetween flees out of the golf ball and the energy is lost. The energy loss which occurs in the interior of the golf ball when the hitting object collides with the golf ball affects the flight distance of the golf ball greatly. Thus the information of the energy loss is useful for improving the restitution performance of the golf ball.
However, since it is very difficult to observe the interior of the golf ball at the time of the collision (impact) between the hitting object and the golf ball, it is impossible to evaluate the energy loss generated in the interior of the golf ball when the hitting object impacts the golf ball. Therefore it is impossible to estimate and observe a portion (for example, a portion of the cover of the golf ball or the center thereof) of the interior of the golf ball and the extent of the generated energy loss. That is, the conventional art is incapable of sufficiently utilizing the energy loss in improving the restitution performance of the golf ball.
In the conventional method of designing the golf ball, a material composing the golf ball is determined, the golf ball is manufactured as an experiment, and the manufactured golf ball is actually hit. In this manner, the restitution performance of the designed golf ball is evaluated. The conventional designing method has a problem that much cost and time are required in the trial manufacture.
The present invention has been made in view of the above-described problem. Thus, it is an object of the present invention to provide a method capable of evaluating an energy loss generated in the interior of a golf ball when an actual hitting object collides (impacts) with the golf ball to improve the restitution performance of the golf ball and facilitate designing thereof.
To achieve the object, the present invention provides a method of evaluating an energy loss of a golf ball, having the steps of dividing a golf ball model into a large number of elements composed of a large number of nodal points in the form of meshes; inputting a physical property of a material for the golf ball; executing a simulation by an analysis based on a finite element method, assuming that a golf club head collides with the golf ball; and computing a strain amount generated in the golf ball model at the time of the collision (first step);
outputting a stress and a strain component of each element of the golf ball model and coordinate values of the nodal points of each element; and momently computing a value of a stress and a strain of each of six components of each element (second step);
finding a relationship between the stress and the strain of each component of each element from the value of the stress and said strain of each of the six components; and computing energy loss values of each element (third step); and
computing the energy loss value for all elements included in the golf ball model; reading the computed energy loss value by a visualizing software; and visualizing the energy loss of said golf ball model (fourth step).
As described above, by visualizing and observing the state of the energy loss generated in the interior of the golf ball when the hitting object collides with the golf ball, it is possible to evaluate the energy loss affecting the restitution performance of the golf ball in a high extent. Thereby it is possible to obtain information useful for improving the restitution performance in designing the golf ball. Therefore it is possible to design the golf ball superior in its restitution performance.
By three-dimensionally visualizing and displaying the energy loss of each element computed by the above-described method, it is possible to estimate and observe the interior portion of the golf ball where the energy loss is generated and the extent of the generated energy loss. The energy loss means the loss of a deformation (hysteresis) of each component of each element.
Since a simulation is executed by using the finite element method, it is possible to save the cost and time necessary for trial manufacture and achieve designing of the golf ball having various constructions by using various materials in a short period of time.
A golf ball model is divided into a large number of elements composed of a large number of nodal points in the form of meshes; a physical property of a material for the golf ball is inputted; a simulation is executed by an analysis based on a finite element method, assuming that a golf club head collides with the golf ball; and a strain amount generated in the golf ball model at the time of the collision is computed.
In executing the analysis based on the finite element method, an initial condition is set on the golf ball model. More specifically, the initial condition includes the size, configuration, construction, and physical property of the golf ball model; and the speed, configuration, construction, and physical property of an object (for example, golf club head model) which collides with the golf ball model.
A stress and a strain component of each element of the golf ball model and coordinate values of the nodal points of each element are outputted; and a value of a stress and a strain of each of six components of each element are computed momently.
In a three-dimensional space, each of the strain and the stress is constituted of three components in a vertical direction and three components in a shear direction, namely, six components in total. Therefore in the simulation executed by the finite element method, the energy loss of each of the elements constituting the golf ball model is computed for the six components. Thereby it is possible to execute an analysis in almost the same state as that generated in the collision between the actual hitting object and the golf ball. Thus the simulation can be accomplished with high accuracy.
In executing the simulation by using the finite element method, the element coordinate system may be used as the coordinate system constituting the reference of the three components of the stress and the strain of each element of the golf ball model in each of the vertical and shear directions in a three-dimensional space. That is, coordinate values of the nodal points of each element necessary for an element coordinate conversion may be outputted; and a value of a stress and a strain of each of six components of each element in an element coordinate system may be computed momently. The coordinate axis moves owing to a rotary movement generated in each element of the golf ball caused by a deformation of the golf ball at the time of the collision between the golf ball and the hitting object. Thus the element coordinate system allows the coordinate axis to move according to the rotary movement of each element. Thereby it is possible to eliminate the influence caused by the rotation of the element and consider only the deformation of the golf ball.
In the case where the element of the golf ball model has the rotary movement owing to the collision between the golf ball model and the hitting object, the influence of the rotary movement of the element of the golf ball is included in a computation performed to find the energy loss by executing the analysis of the six components, based on the finite element method when the element coordinate system is not used but an entire coordinate system is used. In the case where the influence of the rotary movement is removed and energy loss in each direction are computed, the three components in each of the vertical direction and the shear direction in the element coordinate system are computed to find the energy loss favorably.
The relationship between the stress and the strain of each component of each element is found from the value of the stress and the strain of each of the six components; and energy loss values of each element are computed.
More specifically, a stress-strain curve is drawn momently from the relationship between the stress and the strain of each component of each element. A point at which the absolute value of the strain is maximum is found from the stress-strain curve. Thereafter a point at which the absolute value of the strain is maximum is found to compute a work amount done during an increase in the amount of the strain from zero to the maximum absolute value thereof in relation to the time of the collision between the actual hitting object and the golf ball model, and also compute a work amount done in a strain-decrease direction, namely, the work amount done during a decrease in the amount of the strain from its maximum absolute value to zero. The value of the energy loss can be computed from these two work amounts.
Because each of the six components has an energy loss value, the total of the energy loss values of the six components is the energy loss value of the element.
The energy loss value is computed for all elements included in the golf ball model; the computed energy loss value is read by a visualizing software; and the energy loss of the golf ball model is visualized.
As a method of realizing the visualization of the energy loss, a visualizing software xe2x80x9censightxe2x80x9d and the like can be used. This software allows energy losses of each ball-constituting element to be displayed in different colors on a view (contour view).
In visualizing the energy loss, a deformed configuration of the golf ball model is displayed based on coordinate values of nodal points of each element. Thereby it is possible to visualize the energy loss of the golf ball and the configuration thereof at the time of the collision between the golf club head and the golf ball. Thus the method of the present invention is effective for designing the golf ball.
To visualize the energy loss, it is preferable to realize the visualization by classifying different energy loss values by color (color is gradually changed from a warm color to a cold color in dependence on energy loss values) and displaying the difference in energy losses in different colors on the contour view. Thereby it is possible to evaluate the energy loss at a look and clearly.
In measurement which is conducted by the split Hopkinson""s bar tester, a specimen can be strained in a high extent and at a high speed. Therefore the physical property of a material composing the golf ball can be measured in a condition of a strain, a strain speed, and a stress equivalent to those generated in the material when the golf ball is actually hit with an actual golf club head. By using the material having the physical property measured by split Hopkinson""s bar tester, it is possible to simulate the state of a strain and a stress to which the material of the golf ball is subjected, by executing an analysis based on the finite element method. Thus it is possible to visualize the energy loss of the golf ball with high accuracy.
It is preferable to execute the analysis by using a material having a physical property measured in a condition in which its maximum compression strain is 0.05-0.50 and its maximum strain speed is 500/s to 10000/s and favorably 500/s-5000/s, in supposition of a maximum compression strain and a maximum strain speed to be generated when the golf ball is hit with the golf club head. Since the material is measured in the condition of the strain and the strain speed to be generated in a high extent and at a high speed, the evaluation method of the present invention is capable of improving evaluation accuracy.
Needless to say, the physical property of the material for the golf ball model may be measured by a measuring method other than the split Hopkinson""s bar tester, provided that the measuring method is capable of straining a specimen in a high extent and at a high speed and measuring the physical property in the condition of the maximum compression strain and the maximum strain speed equivalent to those to be generated when the golf ball is actually hit with an actual golf club head.
As the physical properties of a material which are used for the analysis based on the finite element method, it is preferable to use those relating to rigidity and viscosity thereof such as Young""s modulus, a shear coefficient, a viscosity coefficient, a loss factor, and the like. It is possible to evaluate the energy loss of the golf ball with high accuracy by using any one of the above-described physical properties or a combination thereof for the analysis based on the finite element method.
In the finite element method, the object (golf ball model) to be analyzed is divided into a large number of elements in the form of mesh. It is favorable to divide the entire golf ball model into 1000-100000 elements, more favorable 25000-60000 elements and very more favorable 25000-20000 elements. The upper limit value is set in view of the capability of a computer currently available. As the capability of the computer is improved, the time required to execute the analysis based on the finite element method is reduced. Thus needless to say, the upper limit value can be changed.
It is preferable that the element is a hexahedron. In view of analysis accuracy, it is favorable that the element is as small as possible. However, the smaller the element is, the longer it takes to perform a computation.
For example, the following method of defining or determining the finite element method is preferable: A first axis of the element coordinate is determined from two nodal points included in the element. Then a plane is defined with the first axis and another nodal point. A line orthogonal to the first axis and normal to the plane xcex1 is set as a second axis. An axis vertical to both the first axis and the second axis is set as a third axis. The element coordinate is determined with the first axis, the second axis, and the third axis.
The method of the present invention is capable of simulating a so-called one-piece golf ball consisting of one layer such as cross-linked rubber layer, a so-called two-piece golf ball composed of two layers such as the cross-linked rubber layer and a cover covering the cross-linked rubber layer, and a so-called multi-piece golf ball composed of three or more layers. That is, the method of the present invention is capable of simulating golf balls having any structure.
Any kind of material which is used for the golf ball can be used as the material for the golf ball which is simulated by the present invention. The material may contain various additives. That is, it is possible to apply a material whose physical property necessary for the analysis based on the finite element method can be measured to the golf ball which is simulated by the present invention.